Visualizing
Linear Functions (II)
Problem:
Suppose that the variable y is a linear function of x with
y = f (x) = mx + b. Given the following table
for the function, move the points (A, B) and (C,D) on the cartesian graph to
match the ordered pairs of data in the table.
- Based on this information, use the point (E,F) on the cartesian graph
(or the related transformation figure) to
a) estimate f (0).
b) estimate the value of an x so that f (x) = 0.
[Notice that, unlike the previous problem type, the point (E,F) is not constrained
in the figure to lie on the line determined by (A,B) and (C,D).]
Describe how the solutions
in problem 1 are related to the positions of E and F on the transformation
figure for f.